Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
262 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 82. C8×C71 | Q32 | semidirect |
| 105. C71 | #12504 | semidirect |
| 180. C8 | #14556074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590613 | 2 |
| #22590592 | 2 |
| #22590569 | 2 |
| #22590567 | 2 |
| #22587937 | 2 |
| C8×C71⋊C16 | 2 |
| C71×#1707 | 2 |
| #12504 | 71 |